I would like to calculate the bending stiffness of a combination of two tubes (of a heart catheter) I have a tube and within that tube there is another tube. The two are not fixed, but the inner tube lies "free" in the outer tube. There is space (air) between the two tubes. I know the geometry and the E modulus of both tubes, and i know how to calculate the bending stiffness EI of the separate tubes. But how does this work with the combination of the two. Where can I find theory about such cases.

For two beams without shear transfer, when calculating stiffness or stresses, you simply add them together. If both beams had the same bending stiffness, the combined ones would simply have double that stiffness. Yours are almost certainly not the same stiffness, but the concept is the same - just add them.

One wrinkle in your case is the space between them. Before they contact each other, the effective stiffness would be just due to the outside tube. Once they contacted, however, you would then add the stiffness of the small tube as well.

Not exactly. You have to take into account the fact that the curvatures of each are not the same ( the tacit assumtion used in adding the stiffness). To get a handle on this, I would assume some reasonable moment assuming the outer tube takes the full moment , get the "curvature" of the outer tube, lay out the inner tube riding on the curve to estimate its curvature from which you can get its moment contribution which you iteratively subtract from the outer tube . Then, from this curvature, get the moment contribution of the outer and repeat this iteratively. The ratio of the moments would be the stiffness ratio of the two tubes. I don't think you can do this in closed form. Moreover, I believe the method is moment dependent.
Having made the case, I think as a practical matter I would be inclined to use the outer tube stiffness alone as a reasonable approximation.